Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Yang, Wei; Fang, Xiongjun; Jing, Jiliang

doi:10.1007/s10714-021-02852-w

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…Together with the ADM 3-momentum unchanged under the spherically symmetric perturbations, we know that there is no restriction on V for the spherically symmetric perturbations. Thus we end up with the corollary that the dynamic stability is equivalent to the thermodynamic stability for the spherically symmetric perturbations of the static, spherically symmetric isentropic charged star, which has also been obtained most recently in [25] instead by performing explicit calculations in the spherical coordinates.…”

Section: Thermodynamic Stability and Axisymmetric Perturbationsmentioning

confidence: 76%

Dynamic and thermodynamic stability of charged perfect fluid stars

Shi

Tian

et al. 2023

Class. Quantum Grav.

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We perform a thorough analysis of the dynamic and thermodynamic stability for the charged perfect fluid star by applying the Wald formalism to the Lagrangian formulation of Einstein-Maxwell-charged fluid system. As a result, we find that neither the presence of the additional electromagnetic field nor the Lorentz force experienced by the charged fluid makes any obstruction to the key steps towards the previous results obtained for the neutral perfect fluid star. Therefore, the criterion for the dynamic stability of our charged star in dynamic equilibrium within the symplectic complement of the trivial perturbaions with the ADM $3$-momentum unchanged is given by the non-negativity of the canonical energy associated with the timelike Killing field, where it is further shown for both non-axisymmetric and axisymmetric perturbations that the dynamic stability against these restricted perturbations also implies the dynamic stability against more generic perturbations. On the other hand, the necessary condition for the thermodynamic stability of our charged star in thermodynamic equilibrium is given by the positivity of the canonical energy of all the linear on-shell perturbations with the ADM angular momentum unchanged in the comoving frame, which is equivalent to the positivity of the canonical energy associated with the timelike Killing field when restricted onto the axisymmetric perturbations. As a by-product, we further establish the equivalence of the dynamic and thermodynamic stability with respect to the spherically symmetric perturbations of the static, spherically symmetric isentropic charged star.

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Section: Thermodynamic Stability and Axisymmetric Perturbationsmentioning

confidence: 76%

Dynamic and thermodynamic stability of charged perfect fluid stars

Shi

Tian

et al. 2023

Class. Quantum Grav.

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“…However, the validity of these assumptions has been proved only for the case in which the background spacetime is static. On the other hand, in support of the entropy principle for the self-gravitating charged perfect fluid [7][8][9][10], only assuming Tolman's law, can one derive the aforementioned ansatz for the local chemical potential from the equation of motion of the fluid. This may give one a misleading impression that these two assumptions are not independent of each other.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields

Shi¹,

Tian²,

Wu³

et al. 2022

Class. Quantum Grav.

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We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.

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Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Cited by 2 publications

References 24 publications

Dynamic and thermodynamic stability of charged perfect fluid stars

Dynamic and thermodynamic stability of charged perfect fluid stars

Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields

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